A Multistage Decomposition Approach for Adaptive Principal Component Analysis

This paper devises a novel neural network model applied to finding the principal components of a N-dimensional data stream. This neural network consists of r(≤ N) neurons, where the i-th neuron has only N–i+1 weights and a N–i+1 dimensional input vector that is obtained by the multistage dimension-reduced processing (multistage decomposition) [7] for the input vector sequence and orthogonal to the space spanned by the first i–1 principal components. All the neurons are trained by the conventional Oja’s learning algorithms [2] so as to get a series of dimension-reduced principal components in which the dimension number of the i-th principal component is N–i+1. By systematic reconstruction technique, we can recover all the principal components from a series of dimension-reduced ones. We study its global convergence and show its performance via some simulations. Its remarkable advantage is that its computational complexity is reduced and its weight storage is saved.

Authors and Affiliations

1. National Lab. of Radar Signal Processing, Xidian University, Xi’an, 710071, China

   Dazheng Feng

Editors and Affiliations

1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

   Jun Wang

2. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, China

   Xiaofeng Liao

3. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

   Zhang Yi

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